Question

Express in terms of sums and differences of logarithms ln 9/8x^8 y

Answer 1

ANSWER


`ln( \frac{9}{8 {x}^(8)y } ) =2ln( {3}) -( 3 ln( {2}) +8 ln( {x}) + ln( y ) )`

Step-by-step explanation

The given logarithmic expression is:


`ln( \frac{9}{8 {x}^(8)y } )`

Recall and apply the quotient rule:


`ln( (a)/(b) ) = ln(a) - ln(b)`

This gives;


`ln( \frac{9}{8 {x}^(8)y } ) = ln( 9 ) - ln( 8 {x}^(8)y )`

Use the product rule:


`ln(ab) = ln(a) + ln(b)`


`ln( \frac{9}{8 {x}^(8)y } ) = ln( 9 ) -( ln( 8 ) + ln( {x}^(8)) + ln( y ) )`


`ln( \frac{9}{8 {x}^(8)y } ) = ln( {3}^(2) ) -( ln( {2}^(3) ) + ln( {x}^(8)) + ln( y ) )`

Apply the power rule:


`ln( {a}^(k) ) = k \: ln(a)`


`ln( \frac{9}{8 {x}^(8)y } ) =2ln( {3}) -( 3 ln( {2}) +8 ln( {x}) + ln( y ) )`